Journal ArticleDOI
A Numerical Method for Solving Matrix Coefficient Heat Equations with Interfaces
Liqun Wang,Liwei Shi +1 more
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TLDR
This method uses the non-traditional finite element method together with finite difference method to get solutions with second-order accuracy and is capable of dealing with matrix coefficient involving time, and the interfaces under consideration are sharp-edged interfaces instead of smooth interfaces.Abstract:
In this paper, we propose a numerical method for solving the heat equations with interfaces. This method uses the non-traditional finite element method together with finite difference method to get solutions with second-order accuracy. It is capable of dealing with matrix coefficient involving time, and the interfaces under consideration are sharp-edged interfaces instead of smooth interfaces. Modified Euler Method is employed to ensure the accuracy in time. More than 1.5th order accuracy is observed for solution with singularity (second derivative blows up) on the sharp-edged interface corner. Extensive numerical experiments illustrate the feasibility of the method.read more
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A Petrov-Galerkin Finite Element Method for Solving the Time-fractional Diffusion Equation with Interface
TL;DR: This paper proposes a Petrov-Galerkin finite element method for solving the two-dimensional time-fractional diffusion equation with interfaces and shows that this method gets to $(2-\alpha)$-order accurate in the $L^2$ and $L^{infty}$ norm.
References
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Journal ArticleDOI
A finite element method for crack growth without remeshing
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Journal ArticleDOI
A level set approach for computing solutions to incompressible two-phase flow
TL;DR: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.
A level set approach for computing solutions to incompressible two- phase flow II
TL;DR: In this article, a level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.
Journal ArticleDOI
Numerical analysis of blood flow in the heart
TL;DR: In this article, the authors extended previous work on the solution of the Navier-Stokes equations in the presence of moving immersed boundaries which interact with the fluid and introduced an improved numerical representation of the δ-function.
Journal ArticleDOI
A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)
TL;DR: A new numerical method for treating interfaces in Eulerian schemes that maintains a Heaviside profile of the density with no numerical smearing along the lines of earlier work and most Lagrangian schemes is proposed.
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